We are interested in the curve fitting problems in such a way that the sum of the squares of the orthogonal distances to the given data points is minimized. Especially, the fitting an ellipse to the given data points is a problem that arises in many application areas, e.g. computer graphics, coordinate metrology, etc. In [1] the problem of fitting ellipses was considered and numerically solved with general purpose methods. In this paper we present another new ellipse fitting algorithm. Our algorithm if mainly based on the steepest descent procedure with the view of ensuring the convergence of the corresponding quadratic function Q(u) to a local minimum. Numerical examples are given.